# Biennial Mode of SST and ENSO

This recent 2016 paper [1] by Kim is supporting consensus to my model of a modulated biennial forcing to ENSO. I had read some of Kim's earlier papers [2] where he introduced the idea of cyclostationary behavior.

The insight that they and I share is that the strictly biennial oscillation is modulated by longer frequencies such that +/- sideband frequencies are created around the 2-year period.

$sin(\pi t) \cdot sin(\omega_m t) = \frac{1}{2} ( cos(\pi t - \omega_m t) - cos(\pi t + \omega_m t) )$
$.$

This is not aliasing but essentially a non-aliased frequency modulation of the base cycle. The insight is clarified by Kim with respect to Meehl's [3] tropospheric biennial oscillation (TBO).

From [1]

That biennial mode locks the base frequency in place to a seasonal cycle, with the modulation creating what looks like a more chaotic pattern. That's why ENSO has been so stubborn to analysis, in that the number of Fourier frequencies doubles with each modulating term. Yet in reality it's likely half as complicated as most scientists have been lead to believe.

Kim also describe the modulated biennial signal in the same terms that I do, via a pair of sideband frequency terms

From [1]

The data analysis they do covers the following region and looks at near-equatorial SST signals (in contrast to the pure ENSO signal):

From [1]

Their isolation of modulating cycles of 11.4 and 4.8 years compare favorably to my ~14.5 and ~6.5 years, especially if you consider Kim's alignment is sloppy in the lower diagram (b); i.e. the peak positions will shift to the left in the south (where ENSO is centered).

From [1]

The most interesting mathematical question surrounding a biennial cycle is that this cycle is metastable with respect to starting on odd or even years. What causes it to pick the parity it chooses, and how stable is that selection?

The breakthrough is that a likely biennial odd/even phase inversion does occur right around 1980, which is in line with the hiccup that Astudillo observe [4]. So if you aren't expecting these phase inversions, you will have a hard time extracting a stationary signal.

My model of biennial modulation for ENSO featuring a phase reversal starting at 1980

Having a mini-consensus like this may propel the discussion toward an understanding that ENSO is likely more deterministically stationary than previously thought.

## References

[1] Kim, Jinju, and Kwang-Yul Kim. "The tropospheric biennial oscillation defined by a biennial mode of sea surface temperature and its impact on the atmospheric circulation and precipitation in the tropical eastern Indo-western Pacific region." Climate Dynamics, 2016: 1-15.    PDF : kim2016.compressed

[2] K.-Y. Kim, J. J. O’Brien, and A. I. Barcilon, “The principal physical modes of variability over the tropical Pacific,” Earth Interactions, vol. 7, no. 3, pp. 1–32, 2003.

[3] G. A. Meehl and J. M. Arblaster, “Relating the strength of the tropospheric biennial oscillation (TBO) to the phase of the Interdecadal Pacific Oscillation (IPO),” Geophysical Research Letters, vol. 39, no. 20, 2012.

[4] H. Astudillo, R. Abarca-del-Rio, and F. Borotto, “Long-term non-linear predictability of ENSO events over the 20th century,” arXiv preprint arXiv:1506.04066, 2015.